Method and computer program for identifying a transition in a phase-shift keying or frequency-shift keying signal

ABSTRACT

A system for identifying phase transitions in phase-shift keying signals and frequency transitions in frequency-shift keying signals broadly comprises a memory and a computing element capable of: selecting a portion of the signal to analyze, wherein the signal comprises a plurality of data samples; applying a transform to the signal to obtain a frequency spectrum; determining a maximum frequency spectrum corresponding to a carrier frequency; determining a starting approximation value of a slope of the phase transition; calculating a bounded limit of slopes within which to search for the phase transition; selecting a plurality of lines; calculating a sum for the data samples associated with each of the lines; and based on the sum for the data samples, identifying a line that corresponds to a location of the phase transition.

RELATED APPLICATION

The present application is a continuation patent application and claimspriority benefit, with regard to all common subject matter, ofearlier-filed U.S. non-provisional patent applications titled “METHODAND COMPUTER PROGRAM FOR IDENTIFYING A TRANSITION IN A PHASE-SHIFTKEYING OR FREQUENCY-SHIFT KEYING SIGNAL”, Ser. No. 11/323,835, filedDec. 30, 2005. The identified earlier-filed application is herebyincorporated by reference in its entirety into the present application.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to signal processing. More particularly,the invention relates to identification and recognition of particularfeatures of signals or, more specifically, phase and frequencytransitions within a signal.

2. Description of the Prior Art

Signal extraction is an increasingly growing field of signal processingthat calls for recognition of certain events in a received signal. Theevent may be a particular pattern, or, as in the present invention, asignal or a portion thereof having a certain feature, such as a phasetransition. Often, little is known about the received signal prior toreceipt. In the present invention, it is specifically desired to knowthe existence of any phase transitions or frequency transitionscontained within the signal. A phase transition is where the phasechanges abruptly and either decreases or increases relative to aprevious portion of the signal. Similarly, a frequency transition iswhere the frequency shifts, which is usually where the phasetransitions. Recognition of phase transitions can be specificallyproblematic due to the short length of phase transitions, such that fewdata samples are associated with the phase transition, and the fact thatnoise often masks the phase transition. Data spikes and outliers alsotend to skew the data or otherwise make signal extraction difficult.

Because the data samples associated with a phase transition may be veryfew, a technique that considers outlying data samples that deviate fromthe norm of the data samples associated with the phase transition tendsto skew or otherwise exert heavy influence on the final extracted image.One prior art method of recognizing or extracting the phase transitionis the zero-crossing method, which is discussed in J. Tsui, DigitalTechniques for Wideband Receivers, SciTech Publishing, Inc., 2nd ed.2004, Chpt. 9. The zero-crossing method is problematic, however, becauseit does not ignore or otherwise take into account outliers. Because theoutliers are considered when extracting an image, the final extractedimage may be inaccurate or otherwise negatively influenced.

A technique that considers too many data samples may be equallyproblematic, in that data samples outside the phase transition (oroutside a zone around the phase transition) may introduce a negativeinfluence. This is because such data samples may improperly contributeto the final extracted image.

Other prior art methods include a delta phase method, also discussed inDigital Techniques at page 330. FIG. 1, which is denoted as “prior art,”illustrates unwrapped phase values in the top graph and the averagedelta phase in the bottom graph. The delta phase method described inDigital Techniques computes the phase transition from the unwrappedphase. The delta phase is the next phase minus the present phase. Tosmooth the result, an average is obtained from four delta phases. Fouris chosen so that it produces the best smoothing without compromisingthe resolution. A higher number gives a smoother result but broadens thepeak. The absolute value of the average delta phase is shown, i.e., withthe negative values rectified. Additionally, the DC level of the averagedelta phase is removed.

FIG. 2, also denoted as “prior art,” illustrates the unwrapped phasevalues in the top graph and a magnified result of the average deltaphase method described in Digital Techniques. The plot of the bottomgraph of FIG. 2 shows a broad peak and a less well-defined start and endof the phase transition.

Accordingly, there is a need for an improved method and computer programthat overcomes the limitations of the prior art. More particularly,there is a need for a method and computer program that is not sensitiveto outliers or an excessive number of data samples. There is further aneed for a method and computer program operable to accurately extractphase transitions while ignoring noise that tends to degrade theextracted image.

SUMMARY OF THE INVENTION

The present invention solves the above-described problems and provides adistinct advance in the art of signal processing. More particularly, thepresent invention provides a method and computer program operable toextract a phase transition from a phase-shift keying (“PSK”) signal or afrequency transition from a frequency-shift keying (“FSK”) signal.

As noted below, the present invention will be discussed specificallywith respect to extracting a phase transition from a PSK signal.However, the present invention can also be used to extract a frequencytransition from an FSK signal, and such will be described further below.

With respect to extracting a phase transition from a PSK signal, themethod and computer program of the present invention broadly comprisesthe steps of selecting a portion of the signal to analyze based on anindependent variable, wherein the signal comprises a plurality of datasamples; applying a Fast-Fourier Transform (“FFT”) to the signal toobtain the frequency spectrum; determining a maximum signalcorresponding to a carrier frequency; mixing the carrier frequency so asto translate the carrier frequency to a low frequency; determining anapproximate value of a slope of the phase transition; determining abounded limit of slopes within which to search for the phase transition;selecting a plurality of lines, each having a slope within the boundedlimit and an initial value, where each line passes through at least oneof the data samples; calculating a sum for the data samples associatedwith each of the lines; and based on the sum for the data samples,identifying the line that corresponds to a location of the phasetransition.

The present invention thus allows for very accurate recognition of ashort and abrupt phase transition that may otherwise be masked by noise.In particular, the present invention recognizes that phase transitionshave a pseudo-linear form. With this knowledge, a Radon transform may beapplied to a small number of data samples corresponding to phase valuesto obtain an accurate extraction of the phase transition. Similarly,application of the present invention allows for extraction of frequencytransitions.

BRIEF DESCRIPTION OF THE DRAWING FIGURES

A preferred embodiment of the present invention is described in detailbelow with reference to the attached drawing figures, wherein:

FIG. 1 illustrates a graph of unwrapped phase values and a graph of aphase transition obtained by application of a prior art average deltaphase method;

FIG. 2 illustrates the unwrapped phase values of FIG. 1 and a plot ofthe phase transition obtained by the prior art delta phase method;

FIG. 3 is a graph of unwrapped phase vs. time/sample number,illustrating a plurality of phase values;

FIG. 4 is a flowchart of a plurality of steps performed for implementingthe present invention;

FIG. 5 is a graph illustrating a data sample falling near a Radon lineand further illustrating a distribution disc for determining a weightedvalue of the data sample with respect to the Radon line;

FIG. 6 is a set of graphs illustrating a weighted sum for the Radon linecorresponding to a phase transition and a location of the phasetransition in an unwrapped phase vs. time/sample number graph;

FIG. 7 is a graph of unwrapped phase values vs. time/sample number;

FIG. 8 is a graph illustrating a falling edge Radon sum of the unwrappedphase values of FIG. 7;

FIG. 9 is a graph of a rising edge Radon sum of the unwrapped phasevalues of FIG. 7;

FIG. 10 is a graph of a level Radon sum of the unwrapped phase values ofFIG. 7;

FIG. 11 is a graph illustrating identification of the phase transitionfrom application of the present invention;

FIG. 12 is a block diagram of the components for implementing the methodof the present invention;

FIG. 13 is a graph illustrating a frequency shift in an unwrapped phasevs. time/sample number graph; and

FIG. 14 is a graph illustrating two Radon lines and determination of achange in phase between the Radon lines.

The drawing figures do not limit the present invention to the specificembodiments disclosed and described herein. The drawings are notnecessarily to scale, emphasis instead being placed upon clearlyillustrating the principles of the invention.

DETAILED DESCRIPTION OF THE INVENTION

The present invention is operable to detect, recognize, extract, orotherwise identify one or more phase transitions in a phase-shift keying(“PSK”) signal or one or more frequency shifts in a frequency-shiftkeying (“FSK”) signal. As is well known in the art, a PSK signal changesor modulates a phase of a carrier wave. Similarly, an FSK signal shiftsa frequency between predetermined values. Because PSK and FSK signalshave similar features in that a known parameter is modulated or shifted,for ease of reading, the following description of the present inventionwill discuss PSK signals only. However, it is understood that thepresent invention can also similarly be used and applied to FSK signalsor any other type of signal with a known shift, change, or modulation,as further described below.

The changes or modulations in the phase of the carrier wave of the PSKsignal result in phase transitions 10, as illustrated in FIG. 3. Thephase transition 10 is where the phase changes abruptly and eitherdecreases or increases relative to a previous portion of the signal, andthe phase transition 10 usually occurs where information is encoded. Thephase transition is often, although not always, very short relative to acarrier frequency portion 12 of the signal and is somewhat exaggeratedin FIG. 1 for illustrative purposes. The very short phase transition isconsequently abrupt or rapid as compared to the carrier frequencyportion 12 of the signal. Due to the quick change, the phase transition10 is a high-frequency event. Simple or inexpensive electronic circuitsdo not handle high-frequency events well and tend to scatter or disruptthe data. Therefore, the present invention allows for recognition of thephase transition, notwithstanding the above-discussed complications.

To identify the phase transition 10 in the signal, the present inventionapplies a Radon transform to extract a straight line corresponding tothe phase transition. Application of the Radon transform allowsextraction of the phase transition even though it may be severely maskedby noise. Additionally, because the phase transition is very short ascompared to the carrier frequency, the amount of data samples associatedwith the phase transition is relatively few. The data samples in thephase transition are also often relatively random as compared to thecarrier frequency. The present invention recognizes that a Radontransform, which is usually applied only where straight-line events areclearly evident, can be helpful in identifying rapidly changing,scattered phase transitions.

As is well-known in the art, a Radon transform sums data samples thatfall on or near a given line, as illustrated in FIG. 3 by the line m₁.If the summed value is large, then it implies a heavy concentration ofdata samples falls on or near the line, and therefore, the chosen lineis likely a good “fit” for the data samples, i.e., the line is a goodmathematical representation for the data samples. If the summed value issmall, as illustrated in FIG. 3 by the line m₂, then less data samplesfall on or near the line, and therefore, the chosen line is not a strongmathematical representation for the data samples. As is understood byone with ordinary skill in the art, a “good” fit is relative to thedesired degree of accurate mathematical representation and is often,although not exclusively, represented by a correlation coefficient. Adiscussion of the Radon transform as used with the present invention isprovided in detail below.

As listed in FIG. 4, the method of the present invention broadlycomprises the steps of: selecting a portion of the signal to analyzebased on an independent variable, wherein the signal comprises aplurality of data samples (step 200); applying a Fast-Fourier Transform(“FFT”) to the signal to obtain the frequency spectrum (step 210);determining a maximum frequency spectrum corresponding to the carrierfrequency (step 220); mixing the carrier frequency so as to translatethe carrier frequency to a low frequency (step 230); determining anapproximate value of a slope of the phase transition (step 240);determining a bounded limit of slopes within which to search for thephase transition (step 250); selecting a plurality of lines, each havinga slope within the bounded limit and an initial value, wherein each linepasses through at least one of the data samples (step 260); calculatinga sum of the data samples associated with each of the lines (step 270);and based on the sum for the data samples, identifying the line thatcorresponds to a location of the phase transition (step 280). It isunderstood that these steps need not be performed in the particularorder provided.

The method begins with selecting a portion of the signal to analyzebased on an independent variable (step 200), such as time or an amountof data contained within the signal. Breaking the signal into discretesegments facilitates processing of the signal and allows for a moreaccurate analysis. The signal is preferably analyzed every 100microseconds, with time being the independent variable. The signal maybe analyzed more or less often depending on other suitable criteria,such as processing speed of a computer performing the method of thepresent invention or desired accuracy. Alternatively, the independentvariable may be the amount of data contained within the signal. Othersuitable independent variables may be used as required. As providedherein, the sample number is the sample at a particular time, andtherefore, the Figures provided herein illustrate time/sample number.

Once the portion of the signal to be analyzed is selected, a FastFourier Transform (“FFT”) is applied to the apportioned signal to obtainthe frequency spectrum (step 210), as is well-known in the art. Astrongest or maximum signal from the frequency spectrum is referred toas the carrier frequency 12 (step 220). Frequency is well-known as therate of change of phase, and the rate of change is equivalent to thefirst derivative or slope of phase. Because frequency is the slope ofphase, the carrier frequency 12 often closely corresponds to or is equalto the slope of the phase values with respect to time in between thephase transitions 10, as best illustrated in FIG. 3. Therefore,reference to “carrier frequency” 12 herein is to be understood as theportion of the signal exclusive of the phase transition 10. In broaderterms, reference to “non-transition portion” is to be understood as theportion of the signal exclusive of a “transition.” Because the phasetransitions drop off very rapidly, the slopes of the phase transitionsare a negative of the carrier frequency. Further, because the phasetransitions usually drop off at a known rate or range of rates, theslopes of the phase transitions can be generally estimated.

As can be understood by one with ordinary skill in the art, thefrequency spectrum analysis described above to obtain the carrierfrequency produces frequency values at discrete points. Therefore,estimation of the carrier frequency is limited in accuracy by thespacing between adjacent frequency components, commonly referred to asbins. Because the bin spacing is often too wide for the desired accuracyof the carrier frequency, a method for obtaining a much more accuratecarrier frequency is provided below. Note that the above method ofestimating the carrier frequency could be improved by interpolation, butthis is often still not accurate enough for noisy data. Anothercomplication is that the frequency spectrum for a PSK signal is not justpurely the spectrum of the carrier frequency. Instead, the obtainedfrequency spectrum also contains the spectrum of the phase transitionsencoded within the signal. Thus, estimation of the carrier frequencyfrom the frequency spectrum is a rough estimation. Notably, this roughestimation is sufficiently close enough that a Radon transform can beapplied to obtain the very accurate carrier frequency, as describedbelow.

Prior to applying the Radon transform to obtain the phase transition,the carrier frequency is mixed (step 230). Commonly, after applying theFFT, the carrier frequency has a very high frequency. Analyzing highfrequencies is undesirable, however, because the signal must betransmitted at a high sampling rate, which consequently requires a highcommunication rate. Therefore, mixing of the carrier frequencytranslates the carrier frequency from a high frequency to a lowfrequency, thereby allowing for analysis of fewer data samples. Otherknown methods of reducing the amount of data samples analyzed withoutdegradation of the signal may also be employed.

The Radon transform described below is preferably applied to theunwrapped phase of the signal. The unwrapped phase is where the phasevalues are not limited to ±π and are allowed to rise or increasecontinuously, except for in the phase transition area.

To obtain an accurate extraction of the location of the phasetransition, a starting approximation for a value of the slope of thephase transition within a bounded limit is first calculated (step 240).Commonly, a slope perpendicular to the carrier frequency is a validstarting approximation. With this known value, a bounded limit for arange of slopes can be calculated (step 250), and the Radon transformcan be applied within this bounded limit. Thus, the method comprisesperforming an iteration process by analyzing summed data samples fallingon or near lines having slopes falling within the bounded limit. Thebounds of the bounded limit may encompass any desired values, dependingon the processor speed of the computer employed to perform the method, adesired accuracy, or other suitable criteria.

To determine the bounds of the bounded limit, an exemplary method maytake upper and lower bounds on either side of the slope perpendicular tothe carrier frequency. For example and as illustrated in FIG. 14, if theslope of the non-transition portion 34, which is the carrier frequency12, is 0.3, then the perpendicular slope is −3.33. The method may thenlook for slopes bounded within ±20% of the perpendicular slope, suchthat a lower bound is 20% lower than the perpendicular slope, and anupper bound is 20% higher than the perpendicular slope. Because offiltering effects, these bounds may be skewed accordingly, i.e., thebounds may be rotated counterclockwise for a falling edge and clockwisefor a rising edge, with the falling and rising edges defined below withrespect to a logic for fitting the data samples to a given line.

An alternative method for calculating the bounds for the slope is basedon the slope of the non-transition portion 34, as opposed to theperpendicular slope of the carrier frequency 12. Additionally, thebounds may not be ±20% or even a percentage value but instead may bedecided on a case-by-case basis. Further, the calculation of the boundsmay account for a highest frequency component and may be processedthrough a plurality of iterations to adjust for an optimum bound basedon an evaluation of the best Radon sum behavior, which is discussedbelow. As can be appreciated, calculation of the bounded limit of slopesis thus an iterative process, wherein the present method recognizesusing the slope of the non-transition portion 34 and perpendicular slopeof the carrier frequency 12 as starting points for calculating thebounded limit.

As is understood in the art, a line must have a slope and initial value.Referring generally to FIGS. 7-11, line(s) with given slope(s) areselected to pass through the data sample(s), ((φ,t), of the unwrappedphase diagram of FIG. 7, where φ is the unwrapped phase and t is thetime value. This is equivalent to setting an initial value for the line.Such a method is computationally convenient because there is noadditional effort needed in mapping the Radon sum, discussed below, tothe data samples. Alternatively, initial values may be determined byselecting equally spaced points on the time axis, where the points havethe form (0,nΔt).

Once the bounds for the slope values and the possible initial values areknown, a plurality of lines may be selected (step 260). Referring toFIG. 14, an average of the phase values of the first five data samplesat the start of the non-transition portion 34 determines where to placea line. Increments of this average phase value either up or down providea range where the line may be placed.

As noted above, the slope of the non-transition portion 34 is otherwisereferred to as the carrier frequency 12. To calculate a very accuratevalue of the carrier frequency, a Radon transform can be applied to thedata samples falling within the non-transition portion 34. Preferably, arelatively large number of data samples may be considered forcalculation of the Radon sum. In FIG. 14, to determine the line segment30, all data samples that fall within the corresponding non-transitionportion 34 are considered. These data samples can be easily deduced fromthe near box-like function of FIG. 11, top graph, from which the startand end of the non-transition portion 34 can be determined. Note thatthe line segments 30 illustrated in FIG. 14 are useful for (1) a veryaccurate determination of the carrier frequency; and (2) a magnitude ofthe phase change, which is discussed in more detail below.

Calculation of the carrier frequency via application of a Radontransform eliminates the influence of the phase transition. The phasetransition exists because of encoded information; therefore, if therewas no encoded information, there would be no phase transition, and thesignal would be purely the carrier frequency. If such is the case, thenestimation of the carrier frequency via the FFT frequency spectrumanalysis described above would be sufficiently accurate. However, sincethe present invention addresses recognition and identification of phasetransition, the described method of determining an accurate carrierfrequency via application of the Radon transform is desirable.

A sum of the data samples, herein referred to as a Radon sum, associatedwith each of the given lines is determined (step 270), as discussed inmore detail below. For illustration purposes, FIG. 3 provides a simplegraph of unwrapped phase values plotted against time. The data samplesas discussed herein are the phase values, and more or less data samplesmay be associated with a signal than as illustrated in FIG. 3.

Within the bounded limit of slope values, a plurality of lines withgiven slopes is selected to pass through the data samples or points. Anydata samples lying in proximity to a given line contribute to a weightedsum for the given line, as discussed in more detail below. The line withthe best overall behavior is the line that is the best representation ofthe phase transition 10 and therefore, is the final solution to theoccurrence of the phase transition (step 280). Determination of whatquantifies as the best behavior is further discussed below.

Preferably, the sum for the data values is a weighted sum, wherein forany given line, each of the data samples that fall on or near the givenline is “smeared,” such that a disc 14 of a given distribution iscentered on the data sample, as best illustrated in FIG. 5. The givendistribution may be any well-known statistical distribution, such as,for example, a Gaussian distribution. The greatest value of the Gaussiandistribution of the disc 14 at the intersection with the line is aweighted value of the data sample. In FIG. 5, for example, thedistributions associated with the data sample are D(r), where r is theradial distance from the data sample. (The distance of the data samplefrom the line and the disc 14 is exaggerated in FIG. 5 for ease ofreading). The smallest distance between the data sample and the givenline is x. The contribution of this data sample to the weighed sum isthen D(x). The distribution should be chosen such that as r increases,the value of the function D(r) decreases, such as, for example, aGaussian distribution centered at the data sample. The weighted sum maybe determined by any of several well-known methods and need not belimited to the above-described method.

Any of several methods may be employed to determine the line with thebest overall behavior, i.e., the line that best fits or models the datasamples. For example, the line that best models the data samples may beobtained by selecting the line with a maximum weighted sum amongst allthe lines analyzed within the bounded limit. As illustrated in FIG. 6,the weighted sum for each phase transition corresponds to peaks 16 inthe graph entitled “Radon Sum Identifying Phase Transitions,” and thephase transitions 10 coincide with the peaks 16 when compared againstthe graph entitled “Unwrapped Phase vs. Time/Sample Number of a PSKSignal.” An alternative method of obtaining the line with the bestoverall behavior may comprise selecting the largest mean of the weightedsum for all the phase transitions, with the smallest standard deviationsof the weighted sum for a given slope or line.

The present invention also includes a logic for fitting the data samplesto a given line. In particular, Radon sums are computed using threeranges of slope, referred to as a falling edge slope, a rising edgeslope, and a level slope. The falling edge slope is where the phasetransition is decreasing (the falling edge region), and the rising edgeslope is where the phase transition is increasing (the rising edgeregion).

The level slope corresponds to a slope of the non-transition portion 34of the signal (the non-transition region), otherwise referred to as thecarrier frequency 12. It is called the “level” slope because during thisportion, the slope is usually constant, i.e., neither increasing ordecreasing.

FIG. 7 illustrates a graph of a plurality of unwrapped phase valuesplotted against time. The individual phase values or data samples willbe referred to by their time location. For example, sample number 33 islocated at t=33 on the graph of FIG. 7. For each data sample, a line isdrawn through the sample, and a Radon sum is determined for the line. Inparticular, for each line through each data sample, the Radon sum isobtained by summing the contributions of the two points preceding thedata sample and the two points subsequent to the data sample. As can beunderstood, the Radon sum could be determined by further summing thedata sample itself; however, because each data sample lies on the line,the contribution of the data sample to the particular line would be thesame for all data samples.

To determine in which region a particular data sample lies, thefollowing logic is applied, where F(t) is the Radon sum for the fallingedge; R(t) is the Radon sum for the rising edge; and L(t) is the Radonsum for the level portion, for all t=time. Similarly, f(t) is the valueof a data sample that fits the falling edge; r(t) is the value for adata sample that fits the rising edge; and l(t) is the value for a datasample that fits the level portion. The functions f(t), r(t), and l(t)are then updated by the following logic:

f(t)=F(t), if F(t)>L(t) and F(t)>R(t)

-   -   Otherwise, f(t)=0;

r(t)=R(t), if R(t)>L(t) and R(t)>F(t)

-   -   Otherwise, r(t)=0; and

l(t)=L(t), if L(t)>R(t) and L(t)>F(t)

-   -   Otherwise, l(t)=0.

FIG. 8 illustrates a graph of the falling edge radon sum, f(t). Takingsample 33 again, L(t) is largest as compared to F(t) and R(t), andtherefore, l(t)=L(t). Thus, sample 33 fits the slope for thenon-transition portion better than any other slopes and should thereforebelong to the non-transition portion. For the graph of FIG. 8, the datasamples not belonging to the falling edge region are assigned a Radonsum of 0, according to the logic.

FIGS. 9 and 10 show similar graphs for the rising edge and levelportions. FIG. 9 illustrates the Radon sum for the rising edge for eachdata sample, r(t). As can be seen, the Radon sum is 0 for all datasamples illustrated in the unwrapped phase of FIG. 7. This is becausethere is no rising edge in the phase values provided in FIG. 7.

FIG. 10 illustrates the level Radon sum, l(t), that is where the slopeis constant. As noted above, a level Radon sum corresponds to anon-transition portion of the signal. As can be seen in FIG. 10, onlythe data samples contributing to the falling edge are assigned a valueof 0 according to the above logic.

FIG. 11 provides two graphs, wherein the top graph illustrates theresult of combining the falling edge Radon sum function f(t) and therising edge r(t). As can be seen, the phase transitions are illustratedby the box-like peaks. The bottom graph of FIG. 11 illustrates theunwrapped phase values of the top graph, and a comparison between theunwrapped phase values can be made to the top graph of FIG. 11.

Once the line exhibiting the best overall behavior, i.e., the line thatis the best fit or model of the data samples for the phase transition,is known, the data samples associated with the line and that otherwisefall on or near to the line, herein referred to as the Radon line, areknown to make up the phase transition. From the extracted phasetransitions, a time interval between consecutive phase transitions canalso be obtained. A clustering program may then be used to determine aminimum time interval, which is referred to as the element length. Theinverse of the element length then provides a baud rate or simply“baud.”

The above-described method can be implemented in hardware, software,firmware, or a combination thereof. In a preferred embodiment, however,the method is implemented with a computer program operated by a hostcomputer 18 or other computing element, as illustrated in FIG. 12. Thehost computer 18 may be in communication with a plurality of computingdevices 20 via a communications network 22 and may be any computingdevice, such as a network computer running Windows NT, Novel Netware,Unix, or any other network operating system. The computer program andhost computer 18 illustrated and described herein are merely examples ofa program and computer that may be used to implement the presentinvention and may be replaced with other software and computers orcomputing elements without departing from the scope of the presentinvention.

The computer program of the present invention is stored in or oncomputer-readable medium 24 residing on or accessible by the hostcomputer 18 for instructing the host computer 18 to execute the computerprogram of the present invention described herein. The computer programpreferably comprises an ordered listing of executable instructions forimplementing logical functions in the host computer 18. The executableinstructions may comprise a plurality of code segments operable toinstruct the computer 18 to perform the method of the present invention.It should be understood herein that one or more steps of the presentmethod may be employed in one or more code segments of the presentcomputer program. For example, a code segment executed by the computermay include one or more steps of the inventive method.

The computer program may be embodied in any computer-readable medium 24for use by or in connection with an instruction execution system,apparatus, or device, such as a computer-based system,processor-containing system, or other system that can fetch theinstructions from the instruction execution system, apparatus, ordevice, and execute the instructions. In the context of thisapplication, a “computer-readable medium” 24 may be any means that cancontain, store, communicate, propagate or transport the program for useby or in connection with the instruction execution system, apparatus, ordevice. The computer-readable medium 24 can be, for example, but notlimited to, an electronic, magnetic, optical, electromagnetic, infrared,or semi-conductor system, apparatus, device, or propagation medium. Morespecific, although not inclusive, examples of the computer-readablemedium 24 would include the following: an electrical connection havingone or more wires, a portable computer diskette, a random access memory(RAM), a read-only memory (ROM), an erasable, programmable, read-onlymemory (EPROM or Flash memory), an optical fiber, and a portable compactdisk read-only memory (CDROM). The computer-readable medium 24 couldeven be paper or another suitable medium upon which the program isprinted, as the program can be electronically captured, via forinstance, optical scanning of the paper or other medium, then compiled,interpreted, or otherwise processed in a suitable manner, if necessary,and then stored in a computer memory.

Although the invention has been described with reference to thepreferred embodiment illustrated in the attached drawing figures, it isnoted that equivalents may be employed and substitutions made hereinwithout departing from the scope of the invention as recited in theclaims. For example, although the present invention has beenspecifically discussed with respect to PSK and FSK signals, the presentinvention is applicable to any signal having a phase or frequencytransition.

The phase transitions may also be obtained by computing a best fit linefor consecutive groups of data samples, wherein the number of datasamples is n. The consecutive groups may be separated by a number of mdata samples, and preferably n>m. A slope of the best fit line is thenplotted against time, and peaks in the plot correspond to the phasetransitions.

The present invention has been discussed with application of a Radontransform. As is well-known in the art, the Hough transform is relatedto the Radon transform. (See M. van Ginkel, C. L. Luengo Hendriks, andL. J. van Vliet, A Short Introduction to the Radon and Hough Transformsand How They Relate to Each Other, Technical Report QI-2004-01,Quantitative Imaging Group, Delft University of Technology, Feb. 2004,1-11). The Hough transform can thus also be used to extract phasetransitions from a signal. In applying the Hough transform, the methodand computer program of the present invention iterates through each datasample for a given slope, wherein it is known the slope lies within abounded limit, as discussed above. The contribution of the data sampleto a weighted sum is then projected onto an axis, and the weighted sumfor each line is then transformed onto a time axis. The line having thehighest weighted sum is determined, and peaks along this line identifyphase transitions. Because application of the Hough transform iteratesthrough individual data samples, as opposed to iterating through alldata samples that fall on or near a given line, the Hough transform isespecially advantageous for a sparse data array.

As noted above, the present invention is also operable to detectfrequency transitions or shifts in FSK signals. In an unwrapped phasevs. time/sample number graph, such as is illustrated in FIG. 13, theslope of a line 26 drawn through a set of data samples is the frequencyfor the set of data samples. A frequency transition 28 thus occurs wherethe phase changes from increasing to decreasing, or from decreasing toincreasing, i.e., where the slope of consecutive sets of data sampleschanges.

The line fitted to the data samples is found by applying a Radon orHough transform, as described above for extracting a phase transition.For two consecutive sets of data samples, two lines are found via theRadon transform, as illustrated by the solid lines 26 in FIG. 13. Forthe case of coherent FSK signals with a smooth phase transition, i.e.,where there is no phase discontinuity, the intersection of the lines isthe location of the frequency transition. Application of the Radon orHough transform then allows for a determination of the mark frequency orspace frequency, and an element length can then be determined byidentification of the shortest mark or space period. For non-coherentFSK signals where both the frequency transition and the phase transitionoccur abruptly at the same instance, the lines obtained via applicationof the Radon or Hough transforms also identify such frequency or phasetransitions. Because the slope of the line(s) fall outside the frequencyrange expected for the FSK signal, identification of a line modeling thefrequency or phase transition is facilitated. The use of the Radontransform and Hough transform discussed herein can be extended tomulti-phase PSK signals and multi-frequency FSK signals.

Additionally, the method and computer program described herein can begeneralized to curved events.

The present invention is also operable to determine a frequency andchange in phase of the PSK signal between consecutive phase transitions.From the unwrapped phase vs. time/sample number domain, as illustratedin FIG. 3, a Radon transform with a range of slopes can be applied toapproximate the frequency of the PSK signal. As noted above, frequencyis the rate of change of phase. Therefore, for the unwrapped phasevalues, the slope of the phase values is the frequency. A bounded limitor range of slope values is obtained from the PSK signal by knowing thecarrier frequency via the frequency spectrum analysis discussed above.Similarly, a bounded limit of initial values is obtained by averagingthe phase values after the starting edge, as also discussed above. Todetermine a more accurate frequency, a plurality of lines having therange of slopes and initial values within the bounded limits may beapplied to the unwrapped phase values to determine a line that has thegreatest or maximum sum, i.e., the line that has the largest number ofdata samples that fall on or near the line. The line that gives themaximum sum has the slope that corresponds to the frequency of the PSKsignal. A weighted sum can also be determined as described above, andthe line having the largest weighted sum may then correspond to thefrequency of the PSK signal. Frequencies obtained for eachnon-transition portion can further be averaged to yield more accuratevalues that are less affected by noise.

In FIG. 14, unwrapped phase values are plotted on a phase vs. timegraph. The two solid lines 30 correspond to two consecutive periods.These solid lines are determined via application of the Radon transform,as discussed above. The phase transition 10 lies between the periods,and a distance x between the two solid lines measured along the verticalaxis gives a magnitude of the change in phase between the two periods,referred to as reference numeral 32. For the particular phase valuesillustrated in FIG. 14, the change in phase is approximately equal to π.

Similar to extracting the phase transition, a Hough transform can beused to find the best-fit lines, and such is useful for a sparse dataarray. Further, linear regression techniques, such as a chi-squaremeasure, to obtain a best straight line fit could be used. Unlike forfinding the phase transition, data samples for finding the best-fitlines for the non-transition portion may include all data samplesbetween the start and end of the non-transition portion. The start andend of the non-transition portion are where the transition zone beginsand ends, respectively, and could easily be inferred from the nearbox-like functions illustrated in FIG. 11, top graph.

The following is an alternative and computationally simpler method offinding a change in phase between neighboring periods. As is well known,the signal will have a certain period, and an initial value of the linefor the frequency of the PSK signal also corresponds to the phase of theperiod. Thus, the phase value can be compared to obtained phase valuesfor neighboring periods, and from this a change in phase betweenneighboring periods can be computed.

1. A system for identifying at least one phase transition in aphase-shift keying signal comprising a plurality of data samplescorresponding to phase values, the system comprising: a memory operableto store computing device executable instructions; and a computingdevice operable to— generate a first falling edge region function foreach data sample; generate a first rising edge function for each datasample; generate a first level function for each data sample; generate asecond falling edge function for each data sample, wherein the secondfalling edge function equals the first failing edge function if thefirst falling edge function is greater than the first rising edgefunction and the first level function, and the second falling edgefunction equals zero otherwise; generate a second rising edge functionfor each data sample, wherein the second rising edge function equals thefirst rising edge function if the first rising edge function is greaterthan the first falling edge function and the first level function, andthe second rising edge function equals zero otherwise; and determine thedata sample regions in which the peak values of the second falling edgefunction and the second rising edge function occur.
 2. The system ofclaim 1, wherein the first falling edge function is a Radon sum for afalling edge slope.
 3. The system of claim 2, wherein the Radon sum iscalculated for a plurality of lines through each data sample.
 4. Thesystem of claim 1, wherein the first rising edge function is a Radon sumfor a rising edge slope.
 5. The system of claim 4, wherein the Radon sumis calculated for a plurality of lines through each data sample.
 6. Thesystem of claim 1, wherein the first level function is a Radon sum for alevel slope.
 7. The system of claim 6, wherein the Radon sum iscalculated for a plurality of lines through each data sample.
 8. Aphysical computer-readable medium comprising a set of computing elementinstructions for identifying at least one phase transition in aphase-shift keying signal comprising a plurality of data samplescorresponding to phase values, the computer-readable medium comprising:a code segment operable to be executed by the computing element forgenerating a first falling edge region function for each data sample; acode segment operable to be executed by the computing element forgenerating a first rising edge function for each data sample; a codesegment operable to be executed by the computing element for generatinga first level function for each data sample; a code segment operable tobe executed by the computing element for generating a second fallingedge function for each data sample, wherein the second falling edgefunction equals the first falling edge function if the first fallingedge function is greater than the first rising edge function and thefirst level function, and the second falling edge function equals zerootherwise; a code segment operable to be executed by the computingelement for generating a second rising edge function for each datasample, wherein the second rising edge function equals the first risingedge function if the first rising edge function is greater than thefirst falling edge function and the first level function, and the secondrising edge function equals zero otherwise; and a code segment operableto be executed by the computing element for determining the data sampleregions in which the peak values of the second falling edge function andthe second rising edge function occur.
 9. The system of claim 8, whereinthe first falling edge function is a Radon sum for a falling edge slope.10. The system of claim 9, wherein the Radon sum is calculated for aplurality of lines through each data sample.
 11. The system of claim 8,wherein the first rising edge function is a Radon sum for a rising edgeslope.
 12. The system of claim 11, wherein the Radon sum is calculatedfor a plurality of lines through each data sample.
 13. The system ofclaim 8, wherein the first level function is a Radon sum for a levelslope.
 14. The system of claim 13, wherein the Radon sum is calculatedfor a plurality of lines through each data sample.